A fuel cell system comprises a fuel cell, which as a rule is constructed as a fuel cell stack. The fuel cell acts as galvanic cell, which converts the chemical energy developing during the chemical reaction of hydrogen and oxygen into water into electric energy, and making it available to electric consumers in the form of an electric voltage. To this end, the fuel cell has an anode side and a cathode side, which comprise at least one anode or at least one cathode. As a cathode gas, oxygen-containing gases, in particular air, are usually employed. As an anode gas, hydrocarbons or hydrocarbon-containing gases are frequently employed. For generating an anode gas, the fuel cell system usually comprises a reformer, which generates a reformate gas as anode gas, which can be fed to the anode side by means of a reformate gas line. To this end, a chemical reaction of a fuel with an oxidant gas takes place at high temperatures, as a consequence of which the reformate gas is created. The reformer can additionally comprise a catalytic converter, which realizes the conversion of the oxidant gas and the fuel into the reformate gas. As oxidant gas, air is frequently employed, while fossil fuels are employed as fuel. During a starting operation of the reformer, in particular during a cold start of the reformer, undesirable by-products are created in the reformate gas, which can be deposited on the anode side, in particular on the anode of the fuel cell and thus reduce the efficiency of the fuel cell. This deposition is amplified in particular in that the anode side during the starting operation of the fuel cell system or during the cold start also has low temperatures, which are below an operating temperature.